Discrete Updates Research Articles

Information flow in non-unitary quantum cellular automata

The information flow in a quantum system is a fundamental feature of its dynamics. An important class of dynamics are quantum cellular automata (QCA), systems with discrete updates invariant in time and space, for which an index theory has been proposed for the quantification of the net flow of quantum information across a boundary. While the index is rigid in the sense of begin invariant under finite-depth local circuits, it is not defined when the system is coupled to an environment, i.e.for non-unitary time evolution of open quantum systems. We propose a new measure of information flow for non-unitary QCA denoted the information current which is not rigid, but can be computed locally based on the matrix-product operator representation of the map.

Rate-independent gradient-enhanced crystal plasticity theory — Robust algorithmic formulations based on incremental energy minimization

Numerically robust algorithmic formulations suitable for rate-independent crystal plasticity are presented. They cover classic local models as well as gradient-enhanced theories in which the gradients of the plastic slips are incorporated by means of the micromorphic approach. The elaborated algorithmic formulations rely on the underlying variational structure of (associative) crystal plasticity. To be more precise and in line with so-called variational constitutive updates or incremental energy minimization principles, an incrementally defined energy derived from the underlying time-continuous constitutive model represents the starting point of the novel numerically robust algorithmic formulations. This incrementally defined potential allows to compute all variables jointly as minimizers of this energy. While such discrete variational constitutive updates are not new in general, they are considered here in order to employ powerful techniques from non-linear constrained optimization theory in order to compute robustly the aforementioned minimizers. The analyzed prototype models are based on (1) nonlinear complementarity problem (NCP) functions as well as on (2) the augmented Lagrangian formulation. Numerical experiments show the numerical robustness of the resulting algorithmic formulations. Furthermore, it is shown that the novel algorithmic ideas can also be integrated into classic, non-variational, return-mapping schemes.

An agile radio-frequency source using internal linear sweeps of a direct digital synthesizer.

Agile rf sources are a common requirement for control systems in quantum science and technology platforms. The direct digital synthesizer (DDS) often fills this role by allowing programmable control of the rf signals. Due to limitations of the DDS architecture, implementing an agile rf source requires rapid and precisely-timed programming of discrete updates that restrict the source's agility. Here, we describe a microcontroller-based interface that exploits the DDS's internal linear sweep accumulator to perform both sequential linear sweeps and standard discrete updates at the ∼10μs scale. This allows updates to the swept parameter as fast as every 8ns with greatly reduced communication and memory overhead. We demonstrate the utility of this system by using it as the reference of an optical phase-locked loop to implement rapid, adjustable laser frequency sweeps in a Rydberg electromagnetically induced transparency spectroscopy measurement.

Underwater mobile gravity measurement data processing using continuous-discrete Kalman filter

To solve the data fusion problem in underwater mobile gravity measurement, a direct estimation method based on pose information is proposed. First, the state model is established using the continuous evolution equation of the state. Then, to obtain the space model of the state for data fusion of the measured underwater mobile gravity, the measurement model is constructed according to the external measurement equation. To solve the continuous-discrete space model of the state, the numerical integration method for continuous time updates and the virtual sampling iterative method for discrete observation updates are proposed, which can be used for the time update case and the observation update case, respectively. In this way, the continuous-discrete iterative extended Kalman filter for direct pose estimation is formed. The proposed methods are compared and analyzed based on the motion simulation data of different carrier and inertial measurement unit simulation data for different accuracy levels. The method proposed in this paper has been validated by carrying out the experiments on a lake. The results show that the method proposed in this paper can minimize the effect of accuracy of initial alignment on strapdown gravimetric measurement and shows a better dynamic estimation performance.

A theoretical contribution to the 1D inverse problem of reflection seismograms

Least-squares full-waveform inversion (FWI) is considered in the frequency domain for a set of noise-free observations of time length [Formula: see text] at the surface obeying the 1D wave equation, with a known source. The initial model is of constant velocity. The first iteration, which equals the constant-velocity migration inversion (CVMI), is thoroughly analyzed. In CVMI, for the unit source power spectrum, it is within reach to analytically derive and interpret the mathematical formulas of the first-order partial derivatives of the modeled observations (Jacobian), and the gradient and Gauss-Newton Hessian of the objective function, and learn what information the calculation requires to obtain a successful physical result (i.e., velocity update). We recognize the gradient elements, except the last one, to be sums of reflection-amplitude weighted band-limited sign functions and the Hessian elements, except along the last column and row, to be band-limited, diagonal-centered triangle functions, which for infinite bandwidth reduces to the Kronecker delta function. When the fundamental frequency [Formula: see text] is lacking in the observations, the gradient loses information of the low-wavenumber trend of the velocity update. The Hessian becomes close to singular, and any stabilized inverse has no chance to repair the deficiencies of the gradient caused by any missing low frequency in the observations. FWI is started by applying CVMI. First, Jacobians are modeled by classic reflectivity modeling. Second, the diagonal Hessians can be used for estimating discrete velocity updates. Third, the Jacobian can be modeled in the first-order Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation and by neglecting transmission effects. Finally, single-frequency and low-frequency seismograms can be inverted by using broadband Hessians. The main mathematical findings are developed by simple numerical models and data.

Learning to Approximate Functions Using Nb-Doped SrTiO3 Memristors.

Memristors have attracted interest as neuromorphic computation elements because they show promise in enabling efficient hardware implementations of artificial neurons and synapses. We performed measurements on interface-type memristors to validate their use in neuromorphic hardware. Specifically, we utilized Nb-doped SrTiO3 memristors as synapses in a simulated neural network by arranging them into differential synaptic pairs, with the weight of the connection given by the difference in normalized conductance values between the two paired memristors. This network learned to represent functions through a training process based on a novel supervised learning algorithm, during which discrete voltage pulses were applied to one of the two memristors in each pair. To simulate the fact that both the initial state of the physical memristive devices and the impact of each voltage pulse are unknown we injected noise into the simulation. Nevertheless, discrete updates based on local knowledge were shown to result in robust learning performance. Using this class of memristive devices as the synaptic weight element in a spiking neural network yields, to our knowledge, one of the first models of this kind, capable of learning to be a universal function approximator, and strongly suggests the suitability of these memristors for usage in future computing platforms.

On Leader-Following Consensus in Multi-Agent Systems with Discrete Updates at Random Times

This paper studies the leader-following consensus problem in continuous-time multi-agent networks with communications/updates occurring only at random times. The time between two consecutive controller updates is exponentially distributed. Some sufficient conditions are derived to design the control law that ensures the leader-following consensus is asymptotically reached (in the sense of the expected value of a stochastic process). The numerical examples are worked out to demonstrate the effectiveness of our theoretical results.

Integrated guidance and control for solar sail station-keeping with optical degradation

Current control approaches for solar sail station-keeping on libration point orbits have not considered the degradation of the sail’s optical properties. However, significant optical degradation could lead to poor station-keeping performance or even complete failure. This paper presents an integrated guidance and control strategy to address this problem by updating the reference orbit based on in situ estimation. An exponential optical degradation model is incorporated into the solar radiation acceleration model, and an on-line reference orbit update approach is incorporated into the station-keeping, coupled with an active disturbance rejection controller. The reflection coefficient is estimated on-line and the reference orbit is updated discretely when the optical properties have degraded by a prescribed amount. This strategy provides discrete updates to the reference orbits such that the perturbation due to the optical degradation is maintained within a small range. These smaller perturbations can be dealt with by the controller’s robustness and station-keeping can be sustained for long durations even in the presence of large optical degradation.

Interaction and Engagement with an Anxiety Management App: Analysis Using Large-Scale Behavioral Data.

BackgroundSAM (Self-help for Anxiety Management) is a mobile phone app that provides self-help for anxiety management. Launched in 2013, the app has achieved over one million downloads on the iOS and Android platform app stores. Key features of the app are anxiety monitoring, self-help techniques, and social support via a mobile forum (“the Social Cloud”). This paper presents unique insights into eMental health app usage patterns and explores user behaviors and usage of self-help techniques.ObjectiveThe objective of our study was to investigate behavioral engagement and to establish discernible usage patterns of the app linked to the features of anxiety monitoring, ratings of self-help techniques, and social participation.MethodsWe use data mining techniques on aggregate data obtained from 105,380 registered users of the app’s cloud services.ResultsEngagement generally conformed to common mobile participation patterns with an inverted pyramid or “funnel” of engagement of increasing intensity. We further identified 4 distinct groups of behavioral engagement differentiated by levels of activity in anxiety monitoring and social feature usage. Anxiety levels among all monitoring users were markedly reduced in the first few days of usage with some bounce back effect thereafter. A small group of users demonstrated long-term anxiety reduction (using a robust measure), typically monitored for 12-110 days, with 10-30 discrete updates and showed low levels of social participation.ConclusionsThe data supported our expectation of different usage patterns, given flexible user journeys, and varying commitment in an unstructured mobile phone usage setting. We nevertheless show an aggregate trend of reduction in self-reported anxiety across all minimally-engaged users, while noting that due to the anonymized dataset, we did not have information on users also enrolled in therapy or other intervention while using the app. We find several commonalities between these app-based behavioral patterns and traditional therapy engagement.

In the interest of saving time: a critique of discrete perception.

A recently proposed model of sensory processing suggests that perceptual experience is updated in discrete steps. We show that the data advanced to support discrete perception are in fact compatible with a continuous account of perception. Physiological and psychophysical constraints, moreover, as well as our awake-primate imaging data, imply that human neuronal networks cannot support discrete updates of perceptual content at the maximal update rates consistent with phenomenology. A more comprehensive approach to understanding the physiology of perception (and experience at large) is therefore called for, and we briefly outline our take on the problem.

Efficient Geometric Operations on Convex Polyhedra, with an Application to Reachability Analysis of Hybrid Systems

We present a novel representation class for closed convex polyhedra, where a closed convex polyhedron is represented in terms of an orthogonal projection of a higher dimensional \(\mathcal{H}\)-polyhedron. The idea is to treat the pair of the projection and the polyhedron symbolically rather than to compute the actual described polyhedron. We call this representation a symbolic orthogonal projection, or a sop, for short. We show that fundamental geometrical operations, like affine transformations, intersections, Minkowski sums, and convex hulls, can be performed by simple block matrix operations on the representation. Due to the underlying \(\mathcal{H}\)-polyhedron, linear programs can be used to evaluate sops, e.g. the usage of template matrices easily yields tight over-approximations. Beyond this, we will also show how linear programming can be used to improve these over-approximations by adding additional supporting half-spaces, or even facet-defining half-spaces, to the over-approximation. On the other hand, we will also discuss some drawbacks of this representation, e.g. the lack of an efficient method to decide whether one sop is a subset of another sop, or the monotonic growth of the representation size under geometric operations. The second part deals with reachability analysis of hybrid systems with continuous dynamics described by linear differential inclusions and arbitrary affine maps for discrete updates. The invariants, guards, and sets of reachable states are given as convex polyhedra. First, we present a purely sop-based reachability algorithm where various geometric operations are performed exactly. Due to the monotonic growth of the representation size of the sops, this algorithm is not suited for practical applications. Then we propose a combination of the sop-based algorithm with a support function based reachability algorithm. Accompanied by some simple examples, we show that this combination results in an efficient reachability algorithm of better accuracy than pure support function based algorithm. We also discuss the current limitations of the proposed techniques and chart a path forward which might help us to solve linear programs over huge sops.

Event-driven contrastive divergence for spiking neuromorphic systems.

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However, the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F) neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The recurrent activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP) carries out the weight updates in an online, asynchronous fashion. We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.

SINGLE-LAYER LASER SCANNER FOR DETECTION AND LOCALIZATION OF UNMANNED SWARM MEMBERS

Abstract. In the presented work unmanned vehicles are used for an extra-terrestrial exploration mission. In this scenario a high factor of redundancy for all systems has to be considered. Defective sensors for instance cannot be repaired and any damage has to be compensated through an intelligent use of the remaining sensors and a robust data fusion. Therefore this work proposes the utilization of a singlelayer laser scanner, which is used for Simultaneous Localization And Mapping (SLAM) for the compensation of a defective relative positioning system. An Extended Kalman-Filter (EKF) with error states is used to perform the loosely coupled integration of the estimated states and the measured relative position in discrete updates. Subsequently the improvement of the navigation solution onboard an Unmanned Aerial Vehicles (UAV) can be estimated. The outcomes of a specifically developed simulation will be shown, delivering theoretic results for the proposed method. A flight test is done finally in order to prove the capability of the laser scanner to detect and locate an UAV.

Polyhedral Flows in Hybrid Automata

A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete updates with differential constraints for capturing continuous flows. Formal verification of hybrid automata relies on symbolic fixpoint computation procedures that manipulate sets of states. These procedures can be implemented using boolean combinations of linear constraints over system variables, equivalently, using polyhedra, for the subclass of linear hybrid automata. In a linear hybrid automaton, the flow at each control mode is given by a rate polytope that constrains the allowed values of the first derivatives. The key property of such a flow is that, given a state-set described by a polyhedron, the set of states that can be reached as time elapses, is also a polyhedron. We call such a flow a polyhedral flow. In this paper, we study if we can generalize the syntax of linear hybrid automata for describing flows without sacrificing the polyhedral property. In particular, we consider flows described by origin-dependent rate polytopes, in which the allowed rates depend, not only on the current control mode, but also on the specific state at which the mode was entered. We identify necessary and sufficient conditions for a class of flows described by origin-dependent rate polytopes to be polyhedral. We also propose and study additional classes of flows: strongly polyhedral flows, in which the set of states that can be reached up to a given time starting from a polyhedron is guaranteed to be a polyhedron, and polyhedrally sliced flows, in which the set of states that can be reached at a given time starting from a polyhedron is guaranteed to be a polyhedron. Finally, we discuss an application of the above classes of flows to approximate exponential behaviours.

The Microstructure of Currency Markets: An Empirical Model of Intra-day Return and Bid-Ask Spread Behavior

This paper analyzes the intra-day relationship between bid-ask spreads and “market” return volatility for U.S. Dollar/Deutschemark quotes. We are able to identify a statistically and economically significant “Reverse U-shaped” pattern in the bid-offer spread in 1996. Tests of the stability and ordering of “market” volatility, performed across several different fractions of the day, reveal that variances of intra-day returns are heterogeneous and ordered, declining around the Asian lunch break, increasing steadily during the London morning trading hours, peaking at the opening of New York to subsequently fall with the closing of the European markets. Results also indicate that “market” volatility is significantly higher during intra-day versus overnight periods. Then, we introduce a structural model that attempts to explain those empirical regularities by capturing some currency-specific features of the data: possibly asymmetric and stochastic trading cost structure, discrete directional updates and parameters’ temporal heterogeneity, and by relating the bid-ask spread to different sources of random noise. We evaluate these parameters via GMM using a set of convenient unconditional intra-day moments implied by the basic configuration of the model. Analysis of the resulting estimated patterns reveals that trading costs play a significant role in explaining the intra-day variability of bid and offer currency returns. Inventory considerations appear to be more relevant in the trading morning, while the perceived risk of arrival of informed trades seems more likely to affect the dealers’ cost structure in the afternoon. The contribution of the “true” currency risk to the total variability of posted bid and ask quotes’ returns is not surprisingly highest with the opening of the European markets.

A wavefield extrapolation method for simulating B-scan images

We describe an algorithm which improves the efficiency of simulations of B-scan images involving water path acoustical imaging systems. The method is a hybrid approach in which Rayleigh-Sommerfeld diffraction theory is used to extrapolate the propagated part of the acoustic pressure field back to the transducer while the scattered field produced by the tissue is obtained using a time-domain scattering algorithm. Considerable savings in both CPU time and array storage are achieved by elimination of discrete time updates on the computational grid between the source and the tissue.

A wavefield extrapolation method for simulating B-scan images.

We describe an algorithm which improves the efficiency of simulations of B-scan images involving water path acoustical imaging systems. The method is a hybrid approach in which Rayleigh-Sommerfeld diffraction theory is used to extrapolate the propagated part of the acoustic pressure field back to the transducer while the scattered field produced by the tissue is obtained using a time-domain scattering algorithm. Considerable savings in both CPU time and array storage are achieved by elimination of discrete time updates on the computational grid between the source and the tissue.